I wired everything up and the controls work well, independently; the Leviton dims the T12 3.5W LED bulbs and the Lutron adjusts the fan from low to medium to high.
When both are turned on and I adjust the Lutron speed, the bulbs will sporadically flicker off and on. This does not happen every single time but there's a 50% chance that a flicker occurs when adjusting the fan speed.
Do I have a hardware incompatibility?
One guess is that the Lutron is causing some weird fluctuation on the neutral but I'm no expert.
My second guess is that the leads for the fan versus light is not adequately separated inside the fan housing.
Per request, below is a wiring diagram. I made it from memory so if something looks off then please request clarity.
Adjusting the ceiling fan speed will sometimes make the ceiling light stay on at full brightness after flickering. Turning the Lutron on or off also affects the behavior of the light.
The flicker will also affect a dimmer+light on the same circuit in an adjacent hallway. Same Leviton dimmer but this has a Great Value bulb. This light always returns to normal after a flicker.
Leaving the Lutron on high and using the pull strings on the fan causes zero issues for the bulbs.
There is another light on the same circuit which is not dimmable and it experiences zero flicker.